Play movie, image, or image sequence at specified time?
Image sequence

You can specify the frame one which the image sequence starts with the Start frame property of the the image node:



Video file

I don't know of a way to do this with a video file in the compositor (there is no start frame option on the  movie clip node).

Note that this is a very trivial matter in the VSE (Video Sequence Editor) for still images, image sequences and video files: